What methods, not including the one of characteristic curves and surfaces, can I use to solve first-order quasilinear equations like this one? u_x+u_y=u^2

eukrasicx 2022-09-29 Answered
What methods, not including the one of characteristic curves and surfaces, can I use to solve first-order quasilinear equations like this one?
u x + u y = u 2
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Answers (1)

Matteo Estes
Answered 2022-09-30 Author has 9 answers
d x d t = 1 , letting x(0)=0 , we have x=t
d y d t = 1 , letting y ( 0 ) = y 0 , we have y = t + y 0 = x + y 0
d u d t = u 2 , we have u ( x , y ) = 1 f ( y 0 ) t = 1 f ( y x ) x
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